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		<a class="header-logo header-affix-hide margin-left-no margin-right-no" data-offset-top="213" data-spy="affix">仙人掌树的同构</a>
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                仙人掌树的同构                </h1>
                <p>时间限制：1s&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  空间限制：512MB</p>			</div>
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                                <h3>题目描述</h3><p><div>首先，先介绍仙人掌树。仙人掌树是一张无向图，但是每个节点最多只会在一个环里面，而且这张图的环全部都是简单环，即A-&gt;B-&gt;C-&gt;A这种。</div>
<div>比如下图就是一颗仙人掌树。</div>
<div>&nbsp;<img src="../file/3899_0.png" width="418" height="269" alt="" /></div>
<div>好的，知道了仙人掌树之后，我们现在要计算一个东西。</div>
<div>我们现在已经知道了一个N个节点的仙人掌树，称作为原图。接下来，我们要用1-N的一个排列A[1]-A[N]去变换这棵树，具体的，如果原图中有一条边i-j，那么变换出来的图中必须有一条A[i]-A[j]的边。同样的，如果变换出来的图中有一条A[i]-A[j]的边，那么原图中必有一条i-j的边。（简单而言就是点重新编号）</div>
<div>小A为了超脱宇宙的束缚，必须要知道，有多少种排列，可以使得变换出来的新图和原图是一模一样的，具体的，原图中如果存在一条i-j的边，新图也存在一条i-j的边，新图中存在一条i-j的边，原图中也存在i-j的边。</div>
<div>方案数目答案mod 1000000003。</div>
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<p></p></p><hr/><h3>输入格式</h3><p><div>
<div>第一行有两个正整数，N和M，节点个数和边的个数。</div>
<div>接下来M行，每行有2个正整数S，T，表示一条原图的无向边。数据保证没有重边。</div>
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<p></p></p><hr/><h3>输出格式</h3><p><div>
<div>一行一个正整数表示方案书目。</div>
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<p></p></p><hr/><h3>样例输入</h3><pre>5 5
1 2
2 3
3 4
4 5
1 5</pre><hr/><h3>样例输出</h3><pre>10</pre><hr/><h3>提示</h3><p><div>所有的答案包括(i,(i+1) % 5 + 1,(i+2) % 5 + 1,(i+3) % 5 + 1,(i+4) % 5 + 1)和(i,(i+4) % 5 + 1,(i+3) % 5 + 1,(i+2) % 5 + 1,(i+1) % 5 + 1)这两种类型。每种类型的i可以是12345，所以答案是2*5=10。</div>
<div>N&lt;=1000</div>
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<p></p></p><hr/><h3>题目来源</h3><p>By 佚名提供</p>
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